%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW388+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 03:10:26 PM UTC 2026
% Result : ContradictoryAxioms 106.29s 19.09s
% Output : CNFRefutation 106.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of formulae : 86 ( 69 unt; 0 def)
% Number of atoms : 105 ( 88 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 48 ( 29 ~; 15 |; 1 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 9 con; 0-3 aty)
% Number of variables : 142 ( 16 sgn 78 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_Collect__empty__eq,axiom,
! [X37,X5] :
( hAPP(c_Set_OCollect(X5),X37) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X37,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).
fof(fact_empty__def,axiom,
! [X5] : c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X5),hAPP(c_COMBK(tc_HOL_Obool,X5),c_fFalse)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__def) ).
fof(fact_Collect__def,axiom,
! [X37,X5] : hAPP(c_Set_OCollect(X5),X37) = X37,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(fact_Diff__cancel,axiom,
! [X15,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X15),X15) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__cancel) ).
fof(fact_Collect__neg__eq,axiom,
! [X37,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X37)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X37)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).
fof(help_c__COMBK__1,axiom,
! [X320,X17,X13,X5] : hAPP(hAPP(c_COMBK(X5,X13),X17),X320) = X17,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_double__complement,axiom,
! [X15,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X15)) = X15,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__complement) ).
fof(fact_Compl__UNIV__eq,axiom,
! [X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__UNIV__eq) ).
fof(fact_UNIV__def,axiom,
! [X5] : c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X5),hAPP(c_COMBK(tc_HOL_Obool,X5),c_fTrue)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__def) ).
fof(fact_Zero__not__Suc,axiom,
! [X119] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X119),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
fof(help_c__fNot__1,axiom,
! [X37] :
( ~ hBOOL(X37)
| ~ hBOOL(hAPP(c_fNot,X37)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(help_c__COMBB__1,axiom,
! [X66,X36,X37,X18,X5,X13] : hAPP(hAPP(hAPP(c_COMBB(X13,X5,X18),X37),X36),X66) = hAPP(X37,hAPP(X36,X66)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_add__eq__self__zero,axiom,
! [X120,X119] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X119),X120) = X119
=> X120 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
fof(fact_transfer__nat__int__numerals_I1_J,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I1_J) ).
fof(fact_Pls__def,axiom,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pls__def) ).
fof(fact_converse__converse,axiom,
! [X140,X5,X13] : hAPP(c_Relation_Oconverse(X13,X5),hAPP(c_Relation_Oconverse(X5,X13),X140)) = X140,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__converse) ).
fof(fact_add__Suc__right,axiom,
! [X120,X119] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X119),hAPP(c_Nat_OSuc,X120)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X119),X120)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X119] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X119),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X119,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_n__not__Suc__n,axiom,
! [X120] : X120 != hAPP(c_Nat_OSuc,X120),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(c_0_19,plain,
! [X37,X5] :
( hAPP(c_Set_OCollect(X5),X37) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X37,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(c_0_20,plain,
! [X7425] : c_Orderings_Obot__class_Obot(tc_fun(X7425,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X7425),hAPP(c_COMBK(tc_HOL_Obool,X7425),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(c_0_21,plain,
! [X7399,X7400] : hAPP(c_Set_OCollect(X7400),X7399) = X7399,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_22,plain,
! [X1350,X1351] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1351,tc_HOL_Obool)),X1350),X1350) = c_Orderings_Obot__class_Obot(tc_fun(X1351,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Diff__cancel]) ).
fof(c_0_23,plain,
! [X7447,X7448] : hAPP(c_Set_OCollect(X7448),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7448),c_fNot),X7447)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7448,tc_HOL_Obool)),hAPP(c_Set_OCollect(X7448),X7447)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_24,plain,
! [X7372,X7373,X7374,X7375,X7377] :
( ( hAPP(c_Set_OCollect(X7377),X7375) = c_Orderings_Obot__class_Obot(tc_fun(X7377,tc_HOL_Obool))
| hBOOL(hAPP(X7375,esk179_1(X7375))) )
& ( ~ hBOOL(hAPP(X7372,X7374))
| hAPP(c_Set_OCollect(X7373),X7372) != c_Orderings_Obot__class_Obot(tc_fun(X7373,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])])])]) ).
fof(c_0_25,plain,
! [X17566,X17567,X17568,X17569] : hAPP(hAPP(c_COMBK(X17569,X17568),X17567),X17566) = X17567,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
cnf(c_0_26,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X1),hAPP(c_COMBK(tc_HOL_Obool,X1),c_fFalse)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_29,plain,
! [X1906,X1907] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1907,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1907,tc_HOL_Obool)),X1906)) = X1906,
inference(variable_rename,[status(thm)],[fact_double__complement]) ).
cnf(c_0_30,plain,
hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OCollect(X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_31,plain,
! [X3933] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3933,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X3933,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X3933,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__UNIV__eq]) ).
fof(c_0_32,plain,
! [X7436] : c_Orderings_Otop__class_Otop(tc_fun(X7436,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X7436),hAPP(c_COMBK(tc_HOL_Obool,X7436),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(c_0_33,plain,
! [X119] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X119),
inference(fof_simplification,[status(thm)],[fact_Zero__not__Suc]) ).
fof(c_0_34,plain,
! [X37] :
( ~ hBOOL(X37)
| ~ hBOOL(hAPP(c_fNot,X37)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
cnf(c_0_35,plain,
( hAPP(c_Set_OCollect(X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(X1,esk179_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_36,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_37,plain,
hAPP(c_COMBK(tc_HOL_Obool,X1),c_fFalse) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool),tc_HOL_Obool),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
fof(c_0_38,plain,
! [X17570,X17571,X17572,X17573,X17574,X17575] : hAPP(hAPP(hAPP(c_COMBB(X17575,X17574,X17573),X17572),X17571),X17570) = hAPP(X17572,hAPP(X17571,X17570)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
cnf(c_0_39,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_40,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2) = hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_27]),c_0_27]) ).
cnf(c_0_41,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_42,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X1),hAPP(c_COMBK(tc_HOL_Obool,X1),c_fTrue)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_43,plain,
! [X4408,X4409] :
( X4408 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4409),X4408) != X4409 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero])])]) ).
cnf(c_0_44,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[fact_transfer__nat__int__numerals_I1_J]) ).
cnf(c_0_45,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
fof(c_0_46,plain,
! [X4392] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X4392),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_33])]) ).
fof(c_0_47,plain,
! [X17592] :
( ~ hBOOL(X17592)
| ~ hBOOL(hAPP(c_fNot,X17592)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_34])]) ).
cnf(c_0_48,plain,
( hBOOL(hAPP(X1,esk179_1(X1)))
| X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),tc_HOL_Obool),tc_HOL_Obool) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_27]),c_0_28]) ).
cnf(c_0_49,plain,
hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool),tc_HOL_Obool),X2) = c_fFalse,
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_50,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_51,plain,
hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40]),c_0_40]) ).
fof(c_0_52,plain,
! [X16329,X16330,X16331] : hAPP(c_Relation_Oconverse(X16331,X16330),hAPP(c_Relation_Oconverse(X16330,X16331),X16329)) = X16329,
inference(variable_rename,[status(thm)],[fact_converse__converse]) ).
cnf(c_0_53,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool),tc_HOL_Obool),
inference(rw,[status(thm)],[c_0_41,c_0_28]) ).
cnf(c_0_54,plain,
hAPP(c_COMBK(tc_HOL_Obool,X1),c_fTrue) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(rw,[status(thm)],[c_0_42,c_0_27]) ).
cnf(c_0_55,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != X1
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_56,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(rw,[status(thm)],[c_0_44,c_0_45]) ).
fof(c_0_57,plain,
! [X3087,X3088] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3088),hAPP(c_Nat_OSuc,X3087)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3088),X3087)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
cnf(c_0_58,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_59,plain,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(c_fNot,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_60,plain,
( hBOOL(X1)
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_48]),c_0_49]),c_0_36]) ).
cnf(c_0_61,plain,
hAPP(c_fNot,hAPP(c_fNot,hAPP(X1,X2))) = hAPP(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_50]) ).
cnf(c_0_62,plain,
hAPP(c_Relation_Oconverse(X1,X2),hAPP(c_Relation_Oconverse(X2,X1),X3)) = X3,
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_63,plain,
hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool),tc_HOL_Obool),
inference(rw,[status(thm)],[c_0_53,c_0_40]) ).
cnf(c_0_64,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) = c_fTrue,
inference(spm,[status(thm)],[c_0_36,c_0_54]) ).
cnf(c_0_65,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) != X2
| X1 = hAPP(c_Int_Onat,c_Int_OPls) ),
inference(rw,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_66,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_67,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_58,c_0_56]) ).
fof(c_0_68,plain,
! [X4405] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4405),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X4405,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_69,plain,
! [X120] : X120 != hAPP(c_Nat_OSuc,X120),
inference(fof_simplification,[status(thm)],[fact_n__not__Suc__n]) ).
cnf(c_0_70,plain,
( ~ hBOOL(X1)
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_71,plain,
hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_72,plain,
hAPP(c_fNot,c_fTrue) = c_fFalse,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_63]),c_0_49]),c_0_64]) ).
cnf(c_0_73,plain,
hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) != X1,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]) ).
cnf(c_0_74,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(split_conjunct,[status(thm)],[c_0_68]) ).
fof(c_0_75,plain,
! [X3092] : X3092 != hAPP(c_Nat_OSuc,X3092),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_69])]) ).
cnf(c_0_76,plain,
( c_fFalse = X1
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_70,c_0_60]) ).
cnf(c_0_77,plain,
hAPP(c_fNot,c_fFalse) = c_fTrue,
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_78,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))) != X1,
inference(spm,[status(thm)],[c_0_73,c_0_66]) ).
cnf(c_0_79,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Int_Onat,c_Int_OPls)) = X1,
inference(rw,[status(thm)],[c_0_74,c_0_56]) ).
cnf(c_0_80,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_81,plain,
( c_fTrue = X1
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_76]),c_0_77]) ).
cnf(c_0_82,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_83,plain,
hAPP(c_Nat_OSuc,c_fTrue) = c_fFalse,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81])]) ).
cnf(c_0_84,plain,
hAPP(c_Nat_OSuc,c_fFalse) != c_fTrue,
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_85,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_81]),c_0_80]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW388+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n009.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 09:50:44 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 106.29/19.09 % Version: 3.5.1
% 106.29/19.09 % Preprocessing class: FMLMSLSMSSSNFFN.
% 106.29/19.09 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 106.29/19.09 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 106.29/19.09 % Starting new_bool_3 with 300s (1) cores
% 106.29/19.09 % Starting new_bool_1 with 300s (1) cores
% 106.29/19.09 % Starting sh5l with 300s (1) cores
% 106.29/19.09 % SAT001_MinMin_p005000_rr_RG with pid 1454810 completed with status 0
% 106.29/19.09 % Result found by SAT001_MinMin_p005000_rr_RG
% 106.29/19.09 % Preprocessing class: FMLMSLSMSSSNFFN.
% 106.29/19.09 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 106.29/19.09 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 106.29/19.09 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 106.29/19.09 % No SInE strategy applied
% 106.29/19.09 % Search class: FGHSM-SMLM33-DFFFFFNN
% 106.29/19.09 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 106.29/19.09 % Starting SubtermCWHack with 135s (1) cores
% 106.29/19.09 % Starting SAT001_MinMin_p005000_rr_RG with 150s (1) cores
% 106.29/19.09 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 106.29/19.09 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 106.29/19.09 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 135s (1) cores
% 106.29/19.09 % SAT001_MinMin_p005000_rr_RG with pid 1454851 completed with status 0
% 106.29/19.09 % Result found by SAT001_MinMin_p005000_rr_RG
% 106.29/19.09 % Preprocessing class: FMLMSLSMSSSNFFN.
% 106.29/19.09 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 106.29/19.09 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 106.29/19.09 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 106.29/19.09 % No SInE strategy applied
% 106.29/19.09 % Search class: FGHSM-SMLM33-DFFFFFNN
% 106.29/19.09 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 106.29/19.09 % Starting SubtermCWHack with 135s (1) cores
% 106.29/19.09 % Starting SAT001_MinMin_p005000_rr_RG with 150s (1) cores
% 106.29/19.09 % Preprocessing time : 0.329 s
% 106.29/19.09 % Presaturation interreduction done
% 106.29/19.09
% 106.29/19.09 % Proof found!
% 106.29/19.09 % SZS status ContradictoryAxioms
% 106.29/19.09 % SZS output start CNFRefutation
% See solution above
% 106.29/19.09 % Parsed axioms : 5248
% 106.29/19.09 % Removed by relevancy pruning/SinE : 0
% 106.29/19.09 % Initial clauses : 7530
% 106.29/19.09 % Removed in clause preprocessing : 231
% 106.29/19.09 % Initial clauses in saturation : 7299
% 106.29/19.09 % Processed clauses : 21393
% 106.29/19.09 % ...of these trivial : 549
% 106.29/19.09 % ...subsumed : 7242
% 106.29/19.09 % ...remaining for further processing : 13602
% 106.29/19.09 % Other redundant clauses eliminated : 1352
% 106.29/19.09 % Clauses deleted for lack of memory : 0
% 106.29/19.09 % Backward-subsumed : 284
% 106.29/19.09 % Backward-rewritten : 598
% 106.29/19.09 % Generated clauses : 209220
% 106.29/19.09 % ...of the previous two non-redundant : 198038
% 106.29/19.09 % ...aggressively subsumed : 0
% 106.29/19.09 % Contextual simplify-reflections : 42
% 106.29/19.09 % Paramodulations : 207848
% 106.29/19.09 % Factorizations : 6
% 106.29/19.09 % NegExts : 0
% 106.29/19.09 % Equation resolutions : 1431
% 106.29/19.09 % Disequality decompositions : 0
% 106.29/19.09 % Total rewrite steps : 66453
% 106.29/19.09 % ...of those cached : 48136
% 106.29/19.09 % Propositional unsat checks : 3
% 106.29/19.09 % Propositional check models : 2
% 106.29/19.09 % Propositional check unsatisfiable : 0
% 106.29/19.09 % Propositional clauses : 0
% 106.29/19.09 % Propositional clauses after purity: 0
% 106.29/19.09 % Propositional unsat core size : 0
% 106.29/19.09 % Propositional preprocessing time : 0.000
% 106.29/19.09 % Propositional encoding time : 0.191
% 106.29/19.09 % Propositional solver time : 0.100
% 106.29/19.09 % Success case prop preproc time : 0.000
% 106.29/19.09 % Success case prop encoding time : 0.000
% 106.29/19.09 % Success case prop solver time : 0.000
% 106.29/19.09 % Current number of processed clauses : 6332
% 106.29/19.09 % Positive orientable unit clauses : 1709
% 106.29/19.09 % Positive unorientable unit clauses: 129
% 106.29/19.09 % Negative unit clauses : 1036
% 106.29/19.09 % Non-unit-clauses : 3458
% 106.29/19.09 % Current number of unprocessed clauses: 174643
% 106.29/19.09 % ...number of literals in the above : 320221
% 106.29/19.09 % Current number of archived formulas : 0
% 106.29/19.09 % Current number of archived clauses : 6823
% 106.29/19.09 % Clause-clause subsumption calls (NU) : 5013330
% 106.29/19.09 % Rec. Clause-clause subsumption calls : 2499236
% 106.29/19.09 % Non-unit clause-clause subsumptions : 4545
% 106.29/19.09 % Unit Clause-clause subsumption calls : 220390
% 106.29/19.09 % Rewrite failures with RHS unbound : 0
% 106.29/19.09 % BW rewrite match attempts : 41479
% 106.29/19.09 % BW rewrite match successes : 1319
% 106.29/19.09 % Condensation attempts : 0
% 106.29/19.09 % Condensation successes : 0
% 106.29/19.09 % Termbank termtop insertions : 7257541
% 106.29/19.09 % Search garbage collected termcells : 99009
% 106.29/19.09
% 106.29/19.09 % -------------------------------------------------
% 106.29/19.09 % User time : 15.921 s
% 106.29/19.09 % System time : 0.438 s
% 106.29/19.09 % Total time : 16.359 s
% 106.29/19.09 % Maximum resident set size: 42576 pages
% 106.29/19.09
% 106.29/19.09 % -------------------------------------------------
% 106.29/19.09 % User time : 72.185 s
% 106.29/19.09 % System time : 1.918 s
% 106.29/19.09 % Total time : 74.103 s
% 106.29/19.09 % Maximum resident set size: 12288 pages
% 106.29/19.09 % E exiting
%------------------------------------------------------------------------------